Question: Divide the following complex numbers: $\dfrac{4 e^{\pi i}}{2 e^{2\pi i / 3}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $4 e^{\pi i}$ ) has angle $\pi$ and radius 4. The second number ( $2 e^{2\pi i / 3}$ ) has angle $\frac{2}{3}\pi$ and radius 2. The radius of the result will be $\frac{4}{2}$ , which is 2. The angle of the result is $\pi - \frac{2}{3}\pi = \frac{1}{3}\pi$ The radius of the result is $2$ and the angle of the result is $\frac{1}{3}\pi$.